1. Technical Field
The present invention relates to a flexural vibration piece that is used for various piezoelectric devices, such as vibrators or resonators, oscillators, gyroscopes, and various sensors, and other electronic devices, and vibrates in a flexural vibration mode.
2. Related Art
A flexural vibration mode piezoelectric vibration piece, such as a tuning-fork type piezoelectric vibration piece, generally has a structure in which grooves are formed at the front surface and/or the rear surface of the vibration arm in the longitudinal direction, and excitation electrodes are formed at the inner surfaces of the grooves (for example, see International Publication No. WO00/44092). Such a vibration arm is configured such that an electric field is generated between an excitation electrode at the side surface of the vibration arm and the excitation electrodes in the grooves so as to be widely distributed over the cross-section of the vibration arm, thereby significantly improving electric field efficiency. Therefore, even when the vibration piece is reduced in size, vibration loss can be made small, and the CI value can be suppressed at a low value.
In the flexural vibration mode piezoelectric vibration piece, if loss of vibration energy occurs at the time of flexural vibration of the vibration arm, deterioration in performance, such as an increase in the CI value or a decrease in the Q value, may occur. In order to prevent or reduce loss of vibration energy, a tuning-fork type crystal vibration piece is known in which cutout portions or cutout grooves having a predetermined depth are formed at both side portions of a base portion, from which the vibration arm extends (see JP-A-2002-261575 and JP-A-2004-260718). When vibration of the vibration arm includes a component in the vertical direction with respect to the main face of the vibration arm, that is, the out-plane direction, the cutout portions or cutout grooves of the base portion mitigate vibration leaking from the base portion. Thus, the confinement effect of vibration energy is increased, an increase in the CI value is suppressed, and a variation in the CI value between the vibration pieces is prevented.
Loss of vibration energy also is generated due to thermal conduction caused by a difference in temperature between a contracting portion of the vibration arm which flexural-vibrates and an expanding portion of the vibration arm to which tensile stress is applied. The decrease in the Q value due to thermal conduction is called a thermoelastic loss effect. In order to prevent or suppress the decrease in the Q value, a tuning-fork type vibrator is known in which a groove or a hole is formed on the center line of the vibration arm (vibration beam) having a rectangular cross-section (for example, see Japanese Utility Model Application No. 63-110151).
However, as described in Japanese Utility Model Application No. 63-110151, if a through hole is formed in the vibration arm, undesirably, rigidity of the vibration arm is significantly deteriorated. As described in the related art, in the piezoelectric vibration piece in which grooves are formed at the front and rear surface of the vibration arm on the center line, it is difficult to sufficiently prevent or suppress the decrease in the Q value due to the thermoelastic effect.
The inventors have suggested a flexural vibration piece in which a flexural vibration portion having a rectangular sectional shape and extending from a base portion to flexural-vibrate, that is, a vibration arm, has a first face and a second face, which are opposite each other and alternately expanded and contracted due to flexural vibration, and a third face and a fourth face, which are opposite each other and have grooves. In this flexural vibration piece, the grooves have a depth smaller than the distance between the third face and the fourth face, and the sum of the depths of the grooves is greater than the distance between the third face and the fourth face. The grooves are arranged between the first face and the second face. The grooves are provided in the above-described manner, such that the vibration arm has an S-shaped cross-section. Thus, the thermomigration path between the first face and the second face is extended, and the time until the difference in temperature between the expanding portion and the contracting portion of the vibration arm is mitigated by thermal conduction is extended, thereby suppressing the change in the Q value due to the thermoelastic effect.
It has been found that, at the time of flexural vibration of the vibration arm having an S-shaped cross-section, in which the grooves are formed in the above-described manner, the vibration arm may be displaced in the in-plane direction including the main faces at which the grooves are formed and in the vertical direction with respect to the main faces. FIGS. 9A to 10B schematically show the configuration of a tuning-fork type piezoelectric vibration piece including a vibration arm having an S-shaped cross-section.
A tuning-fork type piezoelectric vibration piece 1 of FIG. 9A has a pair of vibration arms 3 and 4 which extend in parallel from a base portion 2. At the front and rear main faces of the respective vibration arms, first grooves 5a and 6a and second grooves 5b and 6b are formed to extend in the longitudinal direction from the connection portions to the base portion. The first grooves 5a and 6a and the second grooves 5b and 6b have the same width, length, and depth. The piezoelectric vibration piece 1 of the related art is formed integrally of quartz. Of the quartz crystal axes, the electrical axis X is aligned in the width direction of the vibration arms, the mechanical axis Y is aligned in the longitudinal direction of the vibration arm, and the optical axis Z is aligned in the thickness of the vibration piece.
The first grooves 5a and 6a at the front-side main faces are arranged outside in the width direction with respect to the longitudinal center lines i of the vibration arms 3 and 4. That is, the groove at the front-side main face of one vibration arm is arranged on the opposite side to the other vibration arm. The second grooves 5b and 6b at the rear-side main face are arranged inside in the width direction with respect to the longitudinal center lines i of the vibration arms in the longitudinal direction. That is, the groove at the rear-side main face of one vibration arm is arranged to face the other vibration arm. As shown in FIG. 9B, the first grooves 5a and 6a and the second grooves 5b and 6b are provided so as to have a depth greater than half of the thickness of the vibration arms 3 and 4. The first grooves 5a and 6a and the second grooves 5b and 6b are provided so as not to overlap each other when viewed from the front and rear main faces of the vibration arms and so as to overlap each other from when viewed from the side faces. As a result, the vibration arms have an S-shaped cross-section which is line-symmetric with respect to the center line i′ between the vibration arms.
First excitation electrodes (not shown) are respectively formed at the inner surfaces of the first grooves and the second grooves of the vibration arms 3 and 4. Second excitation electrodes (not shown) are respectively formed at both side faces of the vibration arms. The first excitation electrodes of one vibration arm are connected to the second excitation electrodes of the other vibration arm. An alternating-current voltage is applied to the first excitation electrodes and the second excitation electrodes, such that the vibration arms vibrate to approach or move away from each other.
At this time, it has been found that the vibration arms 3 and 4 have the vibration components in the in-plane of the front and rear main faces and the out-plane direction, that is, in the ±Z direction. When the vibration arms are bent to move away from each other, as indicated by the arrows A1 and A2 of FIG. 9B, the vibration arms are also displaced in the −Z direction. When the vibration arms are bent to approach each other, as indicated by the arrows B1 and B2 of FIG. 9B, the vibration arms are also displaced in the +Z direction.
A tuning-fork type piezoelectric vibration piece 7 of FIG. 10A, first grooves 8a and 9a at the front-side main face are arranged on the same sides in the width direction with respect to the longitudinal center lines i of the vibration arms 3 and 4, that is, the left sides in the drawing. Second grooves 8b and 9b at the rear-side main face are arranged on the same sides in the width direction with respect to the longitudinal center lines i of the vibration arms, that is, on the right sides in the drawing. Similarly to the piezoelectric vibration piece 1 of FIGS. 9A and 9B, the first grooves and the second grooves have a depth greater than half of the thickness of the vibration arms 3 and 4. The first grooves and the second grooves are provided so as not to overlap each other when viewed from the front and rear main faces of the vibration arms and so as to overlap each other when viewed from the side faces. Thus, as shown in FIG. 10B, the vibration arms of the piezoelectric vibration piece 7 have an S-shaped cross-section which is point-symmetric with respect to the center point O between the vibration arms.
In the tuning-fork type piezoelectric vibration piece 7, it has been found that, when an alternating-current voltage is applied to the first excitation electrodes formed at the first grooves and the second grooves and the second excitation electrodes at both side faces of the vibration arms, and the vibration arms 3 and 4 vibrate to approach or move away from each other, the vibration arms have the vibration components in the in-plane direction and the out-plane direction, that is, in the ±Z direction. When the vibration arms are bent to move away from each other, as indicated by the arrows A1 and A2 of FIG. 10B, the vibration arm 3 is also displaced in the −Z direction and the vibration arm 4 is also displaced in the +Z direction. When the vibration arms are bent to approach each other, as indicated by the arrows B1 and B2 of FIG. 10B, the vibration arm 3 is also displaced in the +Z direction and the vibration arm 4 is also displaced in the −Z direction.
Referring to FIGS. 9B and 10B, when the cross-sections of each of the vibration arms is divided by the center lines in the X direction and the Z direction, it can be seen that the displacement in the ±Z direction at the time of flexural vibration of the vibration arms is generated to be attracted to a region having a greater mass. Referring to FIG. 9B, in the vibration arm 3, the displacement in the ±Z direction is generated from the center toward the −X and −Z region and the +X and +Z region where the first and second grooves 5a and 5b have a small occupying area. The same is applied to the vibration arm 4 in which the first and second grooves 6a and 6b are arranged to be different from those in the vibration arm 3. This is because the bending moment of the vibration arm is applied toward a region having a greater mass.
The vibration component in the ±Z direction of the vibration arm, that is, the out-plane vibration component, causes loss of vibration energy, that is, vibration leakage. For this reason, the Q value of the vibration piece decreases, and the CI value is deteriorated. In the flexural vibration piece, the reduction in size causes a decrease in the Q value, such that the decrease in the Q value due to vibration leakage interferes with reduction in size and thickness of the vibration piece.